# Kinetic energy Definition and 264 Discussions

In physics, the kinetic energy of an object is the energy that it possesses due to its motion.
It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its acceleration, the body maintains this kinetic energy unless its speed changes. The same amount of work is done by the body when decelerating from its current speed to a state of rest.
In classical mechanics, the kinetic energy of a non-rotating object of mass m traveling at a speed v is

1
2

m

v

2

{\displaystyle {\begin{smallmatrix}{\frac {1}{2}}mv^{2}\end{smallmatrix}}}
. In relativistic mechanics, this is a good approximation only when v is much less than the speed of light.
The standard unit of kinetic energy is the joule, while the English unit of kinetic energy is the foot-pound.

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1. ### Speed or turning point using energy

Homework Statement Please look at the attached screenshot. This problem is really confusing for me and I can't seem to make much sense out of it. Homework Equations Ei = Ef The Attempt at a Solution As you can see, I did get (a). (The other checkmarks, I guessed — there were only two...
2. ### How much work needs to be done on a piano to move it into the bed of a truck?

Homework Statement Movers must push a piano onto a truck, the bed of which is a height 1.35 m above the ground. To do this they will use a frictionless ramp. If the piano has a mass of 1806.0 kg and the movers push it up the slope at a constant velocity, how much work do they need to do on it...
3. ### Elastic collision with particles, find the kinetic energy

Homework Statement A proton strikes a stationary alpha particle (4He nucleus) head-on. Assuming the collision is completely elastic, what fraction of the proton’s kinetic energy is transferred to the alpha particle? Homework Equations Pi = Pf Ki = Kf The Attempt at a Solution Tried finding...
4. ### I Why E=mc^2 is different from E=1/2 mv^2?

Why kinetic energy is ½ m v2? Why it is different from Einstein’s equation for Energy E= m c2?
5. ### Distance traveled with linearly increasing kinetic energy

Homework Statement An object of mass 50 kg gains 20,000,000 joules every second. Devise formulae to find the distance covered at any given point in time, and the time necessary to cover a certain distance. Homework Equations The Attempt at a Solution E = 20,000,000 * t V = (E * 2/50)1/2...
6. ### Formulating the kinetic energy of an object - helical motion

Hi guys, I need your support to formulate the kinetic energy of an object: - having mass m [Kg] - rotating with angular velocity o [rad/sec] referred to an axis t [m] distant (and parallel) to the symmetry axis of the object - moving along the direction of its symmetry axis with a costant...
7. ### Rotation of Rigid Bodies: Rotating stick with disc on top

Homework Statement [/B] A thin cylindrical rod with the length of L = 24.0 cm and the mass m = 1.20 kg has a cylindrical disc attached to the other end as shown by the figure. The cylindrical disc has the radius R = 8.00 cm and the mass M 2.00 kg. The arrangement is originally straight up...
8. ### Do electromagnetic waves have potential and kinetic energy

Do electromagnetic waves have potential and kinetic energy like springs, strings, etc. If so how are they calculated, inter-related? What is the total energy? Are the energies fluctuating over time? I am a physics hobbyist so generally the first answers should come with the least mathematics...
9. ### Find the launch speed of a ball in a spring mechanism

Homework Statement I have a question asking me to find the launch speed of a ball (mass 0.39kg) when released by a spring mechanism made of 2 springs each with force constant 25Nm^-2. they are pulled back 12 cm. the ball is initially at rest. Homework Equations [/B] v^2=u^2+2as f=ma f=kx...
10. ### Relation between boltsmann/gas constant and temperature

so i have been trying to calculate boltsmann constant by assuming the fact that for an ideal gas the equation : PV=nRT is true. i assume that for containing each molecule the wall needs to apply a force. now here is where it get's a little weird. each molocule should be only deflected in the...
11. ### Kinetic energy of a bouncing ball

Homework Statement I'm trying to find the coefficient of restitution (COR) and energy loss upon impact of a bouncing ball, and I'm trying to understand how these relate to each other. Homework Equations COR=sqrt(2gh/2gH) suvat equations (possibly) 1/2mv^2=mgH (using m=0.0585kg, g=9.8) energy...
12. ### Mechanical energy for planet in elliptical orbit around star

Homework Statement A planet is in an elliptical orbit around a star. Which of the following best represents the mechanical energy E_planet of just the planet and the mechanical energy Es_tar-planet of the star-planet system as functions of time for one complete orbit? Homework Equations...
13. ### Which sphere reaches the bottom of the inclined plane first

Homework Statement Two spheres are placed side by side on an inclined plane and released at the same time. Both spheres roll down the inclined plane without slipping. (a) Using FBD, explain what force provides the torque allowing the sphere to roll down the inclined plane. (b) Which sphere...
14. ### Conservation of momentum - with understanding

I just want to state that i DID solve the problem. I just seek understanding of it. I'd be really grateful if someone could answer two of my questions at the end of this post. The problem I've solved here is just to show what I'm dealing with. 1. Homework Statement Object 1 is moving towards...
15. ### Angular momentum with a large wooden turntable

Homework Statement Homework Equations Li = Lf L = I*omega K = (1/2)*(I)*(omega)^2 The Attempt at a Solution [/B] Given that there are no non-conservative forces in action, I am assuming that the two kinetic energies should be equal. However, as shown by my work above, the two values...
16. ### Finding the Kinetic Energy using the mass, radius and initial KE

Information Given:Zero, a hypothetical planet, has a mass of 4.2 x 1023 kg, a radius of 2.8 x 106 m, and no atmosphere. A 10 kg space probe is to be launched vertically from its surface. Question: (a) If the probe is launched with an initial kinetic energy of 5.0 x 107 J, what will be its...
17. ### Change in the Kinetic Energy of a System

The question is to find the change in kinetic energy of a system. the system in use is a pully system with a wooden block on a flat surface attached to a 100g mass. I have calculated force of friction between the block and desk, and using a ticker timer, I have individual speeds at every 0.1 of...
18. ### How close will body approach fixed point charge?

Homework Statement Charged sphere with a mass of 15 mg and charge 2 nC moves with a speed of 15 cm/s towards a fixed point charge of 3 nC. How close will sphere approach charge? Homework Equations K=(1/2)*mv2 U=k*(Q1Q2/r) The Attempt at a Solution So I am not sure I approached correctly but...
19. ### Momentum and Kinetic Energy

Homework Statement On a frictionless, horizontal air table, puck A (with mass 0.250 kg ) is moving toward puck B (with mass 0.360 kg ), that is initially at rest. After the collision, puck A has a velocity of 0.125 m/s to the left, and puck B has velocity 0.655 m/s to the right. I already...
20. ### Kinetic energy of a solid versus a liquid at the same temperature (through a phase change)

Hi. In all of my question, I mean degrees celsius when I say degree. Think we have a 0 degree ice. we give some energy to it (by a heater) and all of it get into a 0 degree water. How does the kinetic and potential energy of the molecules change? In the book in which I saw this question, it...
21. ### Lifting an object, kinetic energy, work and forces

Homework Statement From a physics multiple choice test: "A car is raised to a height of 10 meters. The car is at rest both before and after it has been lifted. The mass of the car is 900 kg. The total work that has been done on the car during the move is" (The right answer is: zero). Wnet...
22. ### Help me find my error in a relativistic kinetic energy calculation

Hi everyone. Given: an asteroid with the mass of 50,000,000 kg, which is moving with the velocity of oh-my-god particle -- 99.99999999999999999999951% of c. Due to relativistic effects, its total kinetic energy will be 1.44 E+36 Joules (Lorentz factor = 3.2 E+11). A hypothetical particle...
23. ### B Coefficient of Restitution

Where does the Coefficient of Restitution equation come from, in terms of the Conservation of Energy? The measure of efficiency is the velocity after the collision divided by the velocity before the collision, but how does it get to that point? I'm trying to view this focused on an object that...
24. ### Displacement of an object with certain Ek stopped by Frictional Force

Please do excuse if certain terms are not the most technical ones as I am translating the problem from another language. Do feel free to kindly inform me of the more technical term that substitues the sloppy one I've used. (And do excuse the generally bad English overall :-)) 1. Homework...
25. ### How to Find the Potential Energy of a Particle # 9 - YouTube

How can one find the potential energy of a particle. The derivation of PE can be done by the fact that change in PE of a particle is equal to negative of work done by a force on the particle. This combined with Kinetic energy work theorem gives us an equation on conservation of mechanical energy.
26. ### Energy required to accelerate itself

Hi. The energy required to accelerate an object of mass ##m## to a speed ##v## is ##E_k=\frac{m}{2} v^2##. But how much energy does an object need to accelerate itself to ##v##? Say, how much fuel (in energy units) does a car need to accelerate to ##v##, if there are no air resistance or...
27. ### Work, Energy, and Power

Homework Statement There are three problems: 1. How much power is required to lift a 10.00 kg barbell at a speed of 3.0 m/s? 2.What is the average power supplied by a 70.0 kg firefighter climbing up a ladder in 10.0 s? 3. A man pulls a wagon with a force directed 22.0˚ above the horizontal...
28. ### I Integration by parts

Hi, I've been following a derivation of relativistic kinetic energy. I've seen other ways to get the end result but I'm interested in finding out where I've gone wrong here: I'm struggling with integrating by parts. The author goes from...
29. ### B Equation dealing with energy?

What is ΔEp = ΔEk + W I have come across this formula, but i haven't seen it before. What is it used for?
30. ### Finding the speed of the block for one and two springs

Homework Statement The spring in the figure (Figure 1) is compressed by length Δx. It launches the block across a frictionless surface with speed v0. The two springs in the figure (Figure 2) are identical to the spring of figure 1. They are compressed by the same length Δx and used to launch...
31. K

### Side kick on a falling object, mechanical energy and work

If an object with 1kg mass falls free (no air drag), from 100 meters high, and the gravitational acceleration is 9.81, then the mechanical energy will be: 1*9.81*100 = 981 joules. The work the gravitational force does on the object will be: 9.81N*100m = 981 joules. Another object with same...
32. P

### Time of Electron/Proton to Radiate Away Half of Their Energy

Homework Statement It is shown in more advanced courses that charged particles in circular orbits radiate electromagnetic waves, called cyclotron radiation. As a result, a particle undergoing cyclotron motion with speed v is actually losing kinetic energy at the rate \frac{dK}{dt} = -...
33. ### Starting height of marble rolling around a loop the loop

Homework Statement The marble rolls down a track and around a loop-the-loop of radius R. The marble has mass m and radius r. What minimum height h must the track have for the marble to make it around the loop-the-loop without falling off? (Use any variable or symbol stated above along with the...
34. ### Inelastic collision, determine ratio KEf/KEi

Consider the following extreme cases for a completely inelastic collision. In each case, determine the approximate ratio KEf/KEi. a) A moving train collides with a stationary car. b) A moving car collides with a stationary train. I do not understand this question, I'm not given masses or...
35. A

### Work and Kinetic Energy

Homework Statement This is a lab I did for physics. In this experiment, a glider starting from rest on an air track is attached to a string. The string is drawn over a pulley with a mass hanger tied to the other end. Work is done by gravity which results in a gain of kinetic energy of the...
36. M

### Why does kinetic energy depend on the frame of reference?

I'm having this discussion with my engineering peers: A ball is sitting on top of a train traveling at, say, 10m/s. The ball has mass of 2kg, for simplicity. The ball's kinetic energy KE relative to ground zero is 1/2 m v^2, or 100J. A person riding on the train picks up the ball and tosses...
37. G

### Electric Potential Energy - Final Velocity

Homework Statement Four protons (each with mass 1.7 10-27 kg and charge 1.6 10-19 C) are initially held at the corners of a square that is 7.1 10-9 m on a side. They are then released from rest. What is the speed of each proton when the protons are very far apart? (You may assume that the...
38. L

### Object on a vertical Ring with spring attached

picture: https://ibb.co/k5P0GG Two objects slide without friction on a circular ring of radius R, oriented in a vertical plane. The heavier object (of mass 3m) is attached to a spring with an unstretched length of zero (admittedly an unphysical assumption) and spring constant k. The fixed end of...
39. ### Which ball has more energy halfway through the track?

2 frictionless tracks have equal length bumps with one going up and the other down. Halfway through the track which one has more energy? Assuming that they started at the same height, I thought that they had the same amount of energy, but since Ball B ends up having a greater velocity at the...
40. ### GPE and escape velocity

Is it necessary to be the kinetic energy greater than gpe to move ( I don't talk about in orbits) Example : Is it will be harder to move an object has a bigger gpe ( same mass but bigger hight from ground). And thanks.
41. J

### Calculate change in KE and momentum (impulse)

Homework Statement I have attached the problem. A 14,000 kg tractor traveling north at 21 km/h turns west and travels 26 km/h. Calculate the change in the tractor's a. kinetic energy b. linear momentum (magnitude AND direction) Homework Equations [/B] delta KE = (1/2)mv^2 - (1/2)mvi^2...
42. J

### Final speed and direction after a collision (elastic+inelastic)

Homework Statement A billiard ball moves at a speed of 4.00 m/s and collides ELASTICALLY with an identical stationary ball. As a result, the stationary ball flies away at a speed of 1.69 m/s. Determine a. the final speed and direction of the incoming ball after the collision b. the direction...
43. P

### Significant Figures with Kinetic Energy Formula?

Homework Statement An object of mass m = 2.3±0.1 kg is moving at a speed of v = 1.25±0.03 m/s. Calculate the kinetic energy (K = 1 /2mv2 ) of the object. What is the uncertainty in K? I am not exactly sure if I used the error equation correctly when I start using Δ(v2). Could someone verify my...
44. K

### Can anyone help with this magnetism problem?

A 2.53*10^(-6) C charged particle with kinetic energy of 0.0929 J is fired into a uniform magnetic field of magnitude 0.147 T. If the particle moves in a circular path of radius 3.38 m, determine its mass in kg. (answer should be within 2*10^-14 kg) The formula r=mv/qb comes to mind where r is...
45. ### A Usage of kinetic energy in proof for E=mc^2

http://bildr.no/view/aWc4dW95 Above is a question that I posted on a school help site. This is the answer I got: https://www.scribd.com/document/352723366/problem-about-usage-of-E-mc-2-for-v-much-smaller-then-c-ans Can you use this answer to show that the type of calculation that I tried in...
46. ### Understanding Drag Force against a non-linear Force

Homework Statement I'd like to understand Drag Force better; but school always ignores it. Thus, I'm asking this purely out of obssession. I'm picturing a scenario where a non-constant force is pushing an object horizontally, ignoring friction. But, I'd like to understand how Drag Force...
47. ### Need help with collision and conservation of momentum problem

Homework Statement Two blocks move along a horizontal frictionless surface and collide head-on with each other. The mass of the first block, moving to the right with speed v is m, and the mass of the second block moving towards the left with speed 3v is 2m. After the collision, the block of...
48. ### Why isn't Kinetic Energy always equal to Potential Energy?

K= ∫mvdv = ∫m dx/dt dv = ∫m dx/dv dv/dt dv = ∫m dv/dt dx = ∫Fdx = U => K=U, why isn't this true? If it is, wouldn't that mean that Kinetic Energy is always equal to Potential Energy?
49. ### What % of PEg must be converted in KE in order to double v?

Homework Statement What % of PEg must be converted in KE in order to double the speed of a pendulum? So I have spent a couple of days trying to figure out this problem (it's a lab), and I can't seem to figure it out. I have asked my physics teacher about it, and he said the answer to the...
50. ### Help in Homework - Kinetic Energy

Homework Statement Problem: http://imgur.com/a/Sw2zA Hi all, I was given this problem as homework and I have almost no clue on how to solve it. I have tried for some time with no luck. Homework Equations We learned about kinetic and potential energy as well as work. W = F*d W = delta KE PE =...